Rare events in networks with internal and external noise

Abstract

We study rare events in networks with both internal and external noise, and develop a general formalism for analyzing rare events that combines pair-quenched techniques and large-deviation theory. The probability distribution, shape, and time scale of rare events are considered in detail for extinction in the Susceptible-Infected-Susceptible model as an illustration. We find that when both types of noise are present, there is a crossover region as the network size is increased, where the probability exponent for large deviations no longer increases linearly with the network size. We demonstrate that the form of the crossover depends on whether the endemic state is localized near the epidemic threshold or not.

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Cited by in corpus (7)

• Large deviations of random walks on random graphs
• Network desynchronization by non-Gaussian fluctuations
• Rare slips in fluctuating synchronized oscillator networks
• Noise-induced tipping under periodic forcing: preferred tipping phase in a non-adiabatic forcing regime
• Most probable transition paths in piecewise-smooth stochastic differential equations
• Multistage onset of epidemics in heterogeneous networks
• Comparison of theoretical approaches for epidemic processes with waning immunity in complex networks